Influence of Aerosol Chemical Composition on Condensation Sink Efficiency and New Particle Formation in Beijing

Relatively high concentrations of preexisting particles, acting as a condensation sink (CS) of gaseous precursors, have been thought to suppress the occurrence of new particle formation (NPF) in urban environments, yet NPF still occurs frequently. Here, we aim to understand the factors promoting and inhibiting NPF events in urban Beijing by combining one-year-long measurements of particle number size distributions and PM2.5 chemical composition. Our results show that indeed the CS is an important factor controlling the occurrence of NPF events, with its chemical composition affecting the efficiency of the background particles in removing gaseous H2SO4 (effectiveness of the CS) driving NPF. During our observation period, the CS was found to be more effective for ammonium nitrate-rich (NH4NO3-rich) fine particles. On non-NPF event days, particles acting as CS contained a larger fraction of NH4NO3 compared to NPF event days under comparable CS levels. In particular, in the CS range from 0.02 to 0.03 s–1, the nitrate fraction was 17% on NPF event days and 26% on non-NPF event days. Overall, our results highlight the importance of considering the chemical composition of preexisting particles when estimating the CS and their role in inhibiting NPF events, especially in urban environments.

Text S1. Comparison between SMPS and DMPS A Scanning Mobility Particle Sizer (SMPS, Model 3936, TSI) and a Differential Mobility Particle Sizer (DMPS, Custom built) were deployed to measure the PNSDs in the size ranges from 14 to 737 nm and 6 to 840 nm, respectively (Fig. S1, Text S1). In addition, a neutral cluster and air ion spectrometer (NAIS, model 4-11, Airel, Estonia) measured the number size distributions of total particles (2.5-42nm) and ions (0.7-42nm). The data from March 1 st , 2018 to May 30 th , 2018 were measured by the SMPS and from June 1 st , 2018 to March 1 st , 2019 by the DMPS. In order to ensure consistency during our continuous measurements, the particle number size distributions (PNSDs) from the two instruments were compared for the following period when they were simultaneously measuring from June 11 th , 2018 to June 30 th , 2018 (Fig. S1). The comparison results show that the average PNSDs matched well (r 2 =0.97. Further, by assuming that the real size distribution during the overlapping measuring period is the average of the size distributions measured by both instruments (PNSD(SMPS+DMPS)/2), a scaling factor method was developed to correct the systematic difference between the two instruments. Thus, the size-segregated ratios of PNSDSMPS (or PNSDDMPS) to PNSD(SMPS+DMPS)/2 during the overlapping measuring period were applied as the size-resolved correction coefficients to calibrate SMPS (or DMPS), respectively.
Text S2. Measurement of particle chemical compositions Black carbon (BC) in PM2.5 was measured using a seven-wavelength Aethalometer (AE33, Magee Scientific Crop.). The non-refractory chemical compositions of fine particles (NR-PM2.5), including organics (Org), sulfate (SO4), nitrate (NO3), ammonium (NH4), and chloride (Chl), were measured using an online Time-of-Flight Aerosol Chemical Speciation Monitor (ToF-ACSM, Aerodyne Research Inc. U.S.) equipped with a PM2.5 aerodynamic lens and a standard vaporizer. Tof-ACSM was frequently calibrated (once in ~1 month) with NH4NO3 for ionization efficiency (IE) and with pure standards of NH4Cl, (NH4)2SO4 for relative ionization efficiency (RIE). During the whole campaign period, stable IE/air beam signals and RIE were achieved (±20% for standard/average IE/air beam), suggesting the stable performance of Tof-ACSM. The average values of RIEs (for sulfate, nitrate, ammonium, and chloride: were 0.86, 1.05, 4.0, and 1.5, respectively). The IE/air beam averaged from all calibrations were used to calculate the concentrations of NR-PM2.5 chemical components. We also excluded positive bias on organic CO2 + due to high levels of NO3. A more detailed description of the Tof-ACSM settings and artefacts' corrections can be found in Cai et al. 2 .
To resolve the SOA component from the Tof-ACSM measurement, two source apportionment methods were applied 1) m/z44 tracer method according to empirical equations from Ng et al. 3 : Where C44 is the equivalent mass concentration of m/z44 (a tracer ion of SOA).
2) The Positive Matrix Factorization (PMF) method: We solved the PMF by the multilinear engine (ME-2) algorithm implemented within the toolkit SoFi, Source Finder. The detailed information on the PMF method was given in Kulmala et al. 4 .
Overall, SOA resolved from the tracer method and that from the PMF method correlated well (r 2 =0.95, Fig. R8, added as Fig. S3 in our revised manuscript), and SOA from the tracer method was used in the further calculation in this study.
Text S3. Comparison between measured by ACSM and converted mass from PNSDs Since the particle chemical composition and size measurements are based on different detection methods, two kinds of diameter definitions were used in parallel throughout this study. The diameter range of the SMPS and DMPS measurements was defined by the electrical mobility diameter (Dm) and the diameter range of the ACSM measurements was defined by the vacuum aerodynamic diameter (Dva). With the assumption of spherical particles, Dva approximately equals Dm multiplied by average particle density (ρparticle_avg = 1.5 g cm -3 in this study). Although the upper cut-off size of the SMPS and DMPS was still smaller than that of the ACSM and the AE33, those instruments were typically considered to be comparable since in most cases PM2.5 concentrations were dominated by PM1 in Beijing (Table S1) 5,6 . This is also consistent with our dataset comparison between mass concentration converted from PNSD and measured PM2.5 (NR-PM2.5 + BC). To convert the particle number size distributions to mass concentration, apart from spherical particle assumption, time varied particle densities by using their measured chemical composition were also applied 7 . The derived time series of the calculated mass concentration from PNSD compared well to PM2.5 measured by ACSM and AE33 (r 2 = 0.88, slope=0.95, Fig. S3), indicating that submicron aerosols dominated the mass of PM2.5 even though possible uncertainties may be created in the particle density calculation and the ignorance of dust and metal elements, which could not be measured by ACSM. In general, the good correlation and slope close to 1 indicated that those instruments performed steadily and in parallel in terms of chemical mass, number, and size distributions of the particles during the measurement period.
Text S4 Measurement of Sulfuric acid (H2SO4) H2SO4 are measured by a Chemical Ionization Atmospheric Pressure interface Time-of-Flight mass spectrometer (CI-APi-TOF, Aerodyne Research, Inc.) equipped with a nitrate chemical ionization source 8 . The signal of H2SO4 is calibrated with known concentrations of gaseous sulfuric acid produced by the reaction of SO2 and OH radicals that are formed by UV photolysis of water vapor, similar to the protocols in previous literature 9 . We obtained a calibration coefficient of 6.07×10 9 molecule cm -3 for our instrument. Detailed information on the instrument and its setting, calibrations, and corrections can be found in Yan et al. 10 .
Text Text S6. Hygroscopicity parameter and Aerosol water content For a given internal mixture, the hygroscopicity parameter (κ) can be predicted by a simple mixing rule on the basis of chemical volume fractions 13 : Here, κi and εi are the hygroscopicity parameters and volume fraction for component i (dry) in the mixture. We derived εi from the particle chemical composition measured by ACSM. Table S2 gave the densities and hygroscopicity parameters for chemical compounds used in this study. The ionpairing scheme presented by Gysel et al. 14 was used to convert the ion mass concentrations to the mass concentrations of their corresponding inorganic salts. The volume fraction of each species was then calculated from the particle mass concentration divided by its density. Unlike inorganic salts, the hygroscopicity of organic aerosols is not well recognized. Primary organic aerosols (POA) are the unoxygenated component and are generally treated as hydrophobic material with κPOA = 0. κ of laboratory-generated secondary organic aerosols (SOA) varied from 0.01 to 0.2, while it was assumed to be 0.1 in many studies. 15 Further, κ for organic aerosols can be calculated. Wu et al. 16 found that κOA for organic aerosols is approximately 0.06 in Beijing, which was used in our study. We further tested the influence of SOA on κ. In the two sensitive tests (Table S2), we calculated the time series of κtest1 and κtest2 during our observation by assuming that SOA has κSOA value of 0.05 and 0.15, respectively. As shown in Fig. S4, the calculated κtest1 and κtest2 were similar to κ using κOA value of 0.06 for organic aerosols.
ISORROPIA model has been extensively applied to predict aerosol water content (AWC) with the input of ambient temperature, relative humidity (RH), as well as the concentrations of chemical components of fine particulate matters 17,18 . In our analysis, the mass concentrations of NH4, SO4, Chl, NO3 were measured by ACSM as well as meteorological conditions measured by a Vaisala Weather station data acquisition system (AWS310, PWD22, CL51, Metcon) were used as input.
Although there are uncertainties on AWC calculation when not considering the influence of Na, Ca, K, and Mg, the uncertainty remains minimal due to the insignificant mass contribution of crustal ions to PM2.5 in Beijing 6,19 .
Text S7. Classification of new particle formation (NPF) events The original method has been introduced by Dal Maso, et al. 20 . However, for this study, the method was modified to fit the criteria in megacities, where the background particle number concentration is rather high and to include observations from sub-3 nm clusters [21][22][23] . The criteria adopted here include: if a burst of sub-3 nm particles is followed by further particle growth reaching diameters exceeding at least 25 nm, the day is classified as an NPF day. When neither a burst of sub-3 nm particles nor the subsequent growth of newly formed particles is observed, the day is classified into a non-NPF day.
Within the 306 days of observations, 122 NPF events were identified.
Text S8. Sulfuric acid proxy We used a recent proxy for H2SO4 derived by Dada et al. 24 based on the physical understanding of the sources and sinks of H2SO4: Here, k1 represents the coefficient of H2SO4 production term due to daytime SO2-OH reaction, k2 is the coefficient of H2SO4 production via stabilized Criegee Intermediates produced by the ozonolysis of alkenes mostly during nighttime. The third term in Equation 2 represents the loss of H2SO4 to CS. The fourth term considers the additional loss of H2SO4 to cluster formation, and k3 represents the clustering coefficient.

Text S9. Total sulfur and sulfur oxidation ratio
To characterize the fraction of sulfur that exist in the particle phase, the sulfur oxidation ratio (SOR) was calculated as the molar ratio of the gas phase ( 2 ) to the sum of gas-phase ( 2 ) and particle phase ( 4 ) according to equation (4): Within a similar CS range, the SOR was substantially higher at elevated AWC, suggesting a more efficient conversion of SO2 to particle-phase sulphate, leaving less gaseous sulfur available for nucleation (Fig. S8). In addition, more gaseous sulfur was transformed to particle-phase on non-NPF days, indicated by the higher sulfur oxidation ratio (Fig. S12).
Text S10. Wet CS, the effectiveness of CS, and parameter αeff To calculate wet CS (CSwet), we estimated the diameter of wet particles (dwet) 25,26 : Where Dp is the measured dry particle diameter. And GF is the hygroscopicity growth factor calculated as follows: Where κ is the size-dependent hygroscopicity parameter, and aw is water activity obtained by: Where σ is the droplet surface tension, Mw is the molecular weight of water, ρw is the density of liquid water, R is the universal gas constant, and T is the temperature. The size-dependent κ, which were assumed to be 0.24, 0.25, 0.28, 0.3, 0.35 for 30, 50, 100, 200, and >250 nm particles based on the measurements in Hyytiälä, a forest station where the hygroscopicity of particles was widely studied 27 . This assumption is comparable to that observed in China 25,28 .
Effectiveness of CS is defined as the ratio between the real CS (CSeffective) and observed CS (CSobserved) in Kulmala et al. 29 . CSeffective is either the same or less than CSobserved since it is still unclear whether all molecular clusters that collide with pre-existing particles also stick with them. Thus, the effectiveness of CS could not be higher than 1. Effectiveness of CS less than 1 indicated that preexisting particles are not effective as expected in removing gaseous precursors.
αeff resolved from the modeled and measured sulfuric acid could be used to indicate the particles' efficiency in removing vapors. However, αeff is a relative value but not the simple effectiveness of CS. The parameter αeff in our study can be also written as the following expression when wet particles are considered.
Where α'eff is the remaining indicator of the effectiveness of CS after wet CS (CSwet) conditions are considered. Since CS was calculated by dry particle number size distributions, which is not the case in the real atmosphere, and αeff was estimated from the modeled and measured sulfuric acid, αeff could be higher than 1.